Calculation of aggregate loss distributions

Estimation of the operational risk capital under the loss distribution approach requires evaluation of aggregate (compound) loss distributions, which is one of the classic problems in risk theory. Closed-form solutions are not available for the distributions typically used in operational risk; however, with modern computer processing power these distributions can be calculated virtually exactly using numerical methods. This paper reviews numerical algorithms that can be successfully used to calculate the aggregate loss distributions. In particular, Monte Carlo, Panjer recursion and Fourier transformation methods are presented and compared. In addition, several closed-form approximations based on moment matching and asymptotic results for heavy-tailed distributions are reviewed.